Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

The Complex Order Fractional Derivatives and Systems Are Non Hermitian

Version 1 : Received: 11 March 2021 / Approved: 15 March 2021 / Online: 15 March 2021 (16:23:56 CET)

How to cite: Ortigueira, M. The Complex Order Fractional Derivatives and Systems Are Non Hermitian. Preprints 2021, 2021030399 (doi: 10.20944/preprints202103.0399.v1). Ortigueira, M. The Complex Order Fractional Derivatives and Systems Are Non Hermitian. Preprints 2021, 2021030399 (doi: 10.20944/preprints202103.0399.v1).

Abstract

This paper discusses the concept of fractional derivative with complex order from the application point of view. It is shown that a fractional derivative is hermitian, if and only if the order is real. The hermitian part of complex order derivatives behave like allpass filters with almost logarithmic phase.

Keywords

Fractional derivative; Derivative order; Hermitian system; Complex order; Liouville derivative

Subject

ENGINEERING, Automotive Engineering

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